Government plans for a new wave of grammar schools and academies could cost councils hundreds of millions in legal fees and conversion expenses, according to new estimates.

The Local Government Association claimed that if every school in England was converted into an academy – self-governing schools or chains with few connections to their local authorities – there would still be “significant one-off and ongoing costs to council taxpayers”.

While the government has pulled back from its demand that all schools be en route to academy status by 2020, Theresa May’s government has proposed a blizzard of free schools and academies, allowing new faith schools restricted to one religion and scrapping rules barring schools from admitting pupils on the basis of ability from age 12.

Richard Watts, chair of the LGA’s children and young people board, said the change in school structures “will have significant financial implications”.

“We have remained strong in our opposition to all forced academisation, and this opposition has been echoed by MPs, teachers and parents,” Watts said.

“The money that councils are predicted to lose could be better spent on recruiting, training and keeping excellent teachers, and making sure children are safe and have the equipment and support they need, in buildings that are fit for purpose.”

Gibb told a meeting of multi-academy trusts: “Some of the schools in your trust may wish to introduce selection by ability. Your trust may consider establishing a new selective free school or you may look to expand using the routes that are already available.”

The LGA surveyed local authorities and calculated that if every school was to be transferred into an academy sponsored by a multi-academy trust or chain, legal fees, human resources and other staffing costs, as well as paying off outstanding debt, would require spending as much as £163m for primary schools and a further £106m for secondary schools.

If, however, schools simply converted as standalone academies into a trust, the cost would be lower: £106m for primaries and £16m for secondaries, to make a total of £122m.

However, there would still be further costs in lost annual income. Because academies receive an 80% rebate on business rates, councils across England would miss out on an additional £80m each year.

The Department for Education (DfE) took issue with some of the LGA’s calculations, arguing that most schools would go via the cheaper “converter academy” option, meaning costs would be at the lower end of the scale.

“We have the funding to ensure more schools can take advantage of the opportunities presented by becoming an academy, with more than £600m available in this parliament to support schools to convert,” a DfE spokesperson said.

“We recognise local authorities and church dioceses will also face costs and funding will also be provided to them. We are considering options for this and will make further information available in due course.”

Kevin Courtney, general secretary of the National Union of Teachers, said the figures “should act as a wake-up call for those advocates of structural school reform for the sake of it.

“This is money that schools desperately need now if they are to provide the world-class education that all our children and young people need and deserve.

“While schools across the country are laying off teachers and support staff and cutting back on essential resources and services, no responsible government should be actively pursuing a policy that has such a high cost and no proven worth,” he said.